Finite Group Databasebeta

← #23764386

Subgroups — #23764386

Order 10112.

324 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19098423C211yesmaximal, characteristic
2C4×C22⋊Dic79C211yesmaximal, characteristic
3#19098330C214yesmaximal
4C2×C22⋊Q8×C79C211yesmaximal, characteristic
5C2×C4⋊Dic79—21no—
6C2×C22⋊Dic79C2212yes—
7C2×C22⋊Dic79C2212yes—
8C2×C4×Dic79—21no—
9C79⋊#95—21no—
10C79⋊#95—21no—
11C22×Q8×C79C411yescharacteristic, complemented
12C23×C4×C79C2211yescharacteristic
13C22⋊Q8×C79—21no—
14C22⋊Q8×C79—21no—
15C22⋊Q8×C79—21no—
16C22⋊Q8×C79—21no—
17C2×C4⋊C4×C79C411yescharacteristic, complemented
18C2×C4⋊C4×C79C412yescomplemented
19C2×C22⋊C4×C79C2212yes—
20C22×Dic79—22no—
21C22×Dic79—22no—
22C4⋊Dic79—42no—
23C22⋊Dic79—22no—
24C22⋊Dic79—24no—
25C22⋊Dic79Q814yescomplemented
26C4×Dic79—42no—
27C24×C79C2311yescharacteristic
28C2×Q8×C79—21no—
29C2×Q8×C79—21no—
30C2×Q8×C79—42no—
31C22×C4×C79—42no—
32C22×C4×C79C2×C411yescharacteristic
33C22×C4×C79C2×C412yes—
34C22×C4×C79C2×C412yes—
35C22×C4×C79C2×C411yescharacteristic
36C22×C4×C79D411yescharacteristic
37C22×C4×C79D411yescharacteristic
38C22×C4×C79D411yescharacteristic
39C22×C4×C79D411yescharacteristic
40C4⋊C4×C79—21no—
41C4⋊C4×C79—21no—
42C4⋊C4×C79—22no—
43C4⋊C4×C79—22no—
44C22⋊C4×C79—22no—
45C22⋊C4×C79—22no—
46C23×C79—41no—
47C23×C79—41no—
48C23×C79C22×C411yescharacteristic
49C23×C79C2×D411yescharacteristic
50C23×C79C2×D411yescharacteristic
51C23×C79C2×Q812yes—
52C23×C79#4112yes—
53Q8×C79—42no—
54Q8×C79—42no—
55C2×C4×C79—22no—
56C2×C4×C79—22no—
57C2×C4×C79—22no—
58C2×C4×C79—22no—
59C2×C4×C79—22no—
60C2×C4×C79—41no—
61C2×C4×C79—41no—
62C2×C4×C79—41no—
63C2×C4×C79—42no—
64C2×C4×C79—42no—
65C2×C4×C79C22⋊C411yescharacteristic
66C2×C4×C79C22⋊C411yescharacteristic
67C2×C4×C79C22⋊C411yescharacteristic
68C2×C4×C79C22⋊C411yescharacteristic
69C2×Dic79—24no—
70C2×Dic79—42no—
71C2×Dic79—42no—
72C2×Dic79—42no—
73C2×Dic79—42no—
74C2×Dic79—42no—
75C22×C79—21no—
76C22×C79—21no—
77C22×C79—21no—
78C22×C79—21no—
79C22×C79—21no—
80C22×C79—21no—
81C22×C79—42no—
82C22×C79—42no—
83C22×C79C2×C22⋊C411yescharacteristic
84C22×C79C4×Q812yes—
85C22×C79C22⋊Q812yes—
86C22×C79#12411yescharacteristic
87C22×C79C4⋊Q811yescharacteristic
88C4×C79—21no—
89C4×C79—21no—
90C4×C79—21no—
91C4×C79—42no—
92C4×C79—42no—
93C4×C79#9912yes—
94Dic79—44no—
95Dic79—82no—
96C2×C79—22no—
97C2×C79—21no—
98C2×C79—22no—
99C2×C79—21no—
100C2×C79#39111yescharacteristic
101C2×C79C2×#9911yescharacteristic
102C2×C79#41011yescharacteristic
103#1996—791nomaximal, Sylow
104C79#199611yescharacteristic, complemented, Sylow
105C2×C22⋊Q8D7911yescharacteristic
106#380—791no—
107C4×C22⋊C4—791no—
108#342—794no—
109C22×Q8Dic7911yescharacteristic, complemented
110C23×C4C2×D7911yescharacteristic
111C22⋊Q8—21no—
112C22⋊Q8—21no—
113C22⋊Q8—21no—
114C22⋊Q8—21no—
115C2×C4⋊C4—1581no—
116C2×C4⋊C4Dic7911yescharacteristic, complemented
117C2×C4⋊C4Dic7912yescomplemented
118C2×C22⋊C4—792no—
119C2×C22⋊C4—792no—
120C2×C22⋊C4C2×D7912yes—
121C2×C42—1581no—
122#95—1581no—
123#95—1581no—
124C24C22×D7911yescharacteristic
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—42no—
128C22×C4—42no—
129C22×C4—1582no—
130C22×C4—1582no—
131C22×C4C2×Dic7911yescharacteristic
132C22×C4C2×Dic7912yes—
133C22×C4C2×Dic7912yes—
134C22×C4C2×Dic7911yescharacteristic
135C22×C4C22⋊D7911yescharacteristic
136C22×C4C22⋊D7911yescharacteristic
137C22×C4C22⋊D7911yescharacteristic
138C22×C4C22⋊D7911yescharacteristic
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—3162no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—794no—
147C22⋊C4—1584no—
148C22⋊C4—1582no—
149C42—3162no—
150C23—41no—
151C23—41no—
152C23C22×Dic7911yescharacteristic
153C23C2×C22⋊D7911yescharacteristic
154C23C2×C22⋊D7911yescharacteristic
155C23Q8×D7912yes—
156C23#1192962512yes—
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—3162no—
170C2×C4—3162no—
171C2×C4—3162no—
172C2×C4—3162no—
173C2×C4—3162no—
174C2×C4—1584no—
175C2×C4C22⋊Dic7911yescharacteristic
176C2×C4C22⋊Dic7911yescharacteristic
177C2×C4C22⋊Dic7911yescharacteristic
178C2×C4C22⋊Dic7911yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C2×C22⋊Dic7911yescharacteristic
188C22Q8×Dic7912yes—
189C22#1457913712yes—
190C22#1457915011yescharacteristic
191C22#1457915911yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—42no—
196C4—42no—
197C4—3164no—
198C4—6322no—
199C4#1457907612yes—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2#1909847011yescharacteristic
205C2C2×#1457907611yescharacteristic
206C2#1909853711yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic79
commutatorC23×C79C22×C4
FrattiniC24C22×D79
FittingC2×C22⋊Q8×C79C2
socleC22×C79C2×C22⋊C4
prime radical, cosocleC24×C79C23
hypercenterC2×C22⋊Q8D79
hypocenterC79#1996
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
11. C22×Q8×C79C4semidirect
17. C2×C4⋊C4×C79C4semidirect
18. C2×C4⋊C4×C79C4semidirect
25. C22⋊Dic79Q8semidirect
104. C79#1996semidirect
109. C22×Q8Dic79semidirect
116. C2×C4⋊C4Dic79semidirect
117. C2×C4⋊C4Dic79semidirect